Approachability in infinite dimensional spaces

Ehud Lehrer ()

International Journal of Game Theory, 2003, vol. 31, issue 2, pages 253-268

Abstract: The approachability theorem of Blackwell (1956b) is extended to infinite dimensional spaces. Two players play a sequential game whose payoffs are random variables. A set C of random variables is said to be approachable by player 1 if he has a strategy that ensures that the difference between the average payoff and its closest point in C, almost surely converges to zero. Necessary conditions for a set to be approachable are presented.

Date: 2003-01-22
Note: Received February 2002/Final version July 2002
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